Temperature and field dependence of the intrinsic tunnelling structure in overdoped Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$

We report intrinsic tunnelling data for mesa structures fabricated on three over- and optimally-doped $\mathrm{B}{\mathrm{i}}_{2.15}\mathrm{S}{\mathrm{r}}_{1.85}\mathrm{C}\mathrm{a}\mathrm{C}{\mathrm{u}}_2{\mathrm{O}}_{8+\delta }$ crystals with transition temperatures of 86-78~K and 0.16-0.19~holes per CuO${}_2$ unit, for a wide range of temperature ($T$) and applied magnetic field ($H$), primarily focusing on one over-doped crystal(OD80). The differential conductance above the gap edge shows clear dip structure which is highly suggestive of strong coupling to a narrow boson mode. Data below the gap edge suggest that tunnelling is weaker near the nodes of the d-wave gap and give clear evidence for strong $T$-dependent pair breaking. These findings could help theorists make a detailed Eliashberg analysis and thereby contribute towards understanding the pairing mechanism. We show that for our OD80 crystal the gap above $T_c$ although large, is reasonably consistent with the theory of superconducting fluctuations.